mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
58 lines
1.5 KiB
C
58 lines
1.5 KiB
C
/*
|
|
Copyright (C) 2016 Pascal Molin
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb is free software: you can redistribute it and/or modify it under
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "acb_dirichlet.h"
|
|
|
|
void
|
|
acb_dirichlet_root_number_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
|
|
{
|
|
arb_t x;
|
|
acb_t eps;
|
|
|
|
arb_init(x);
|
|
arb_one(x);
|
|
acb_dirichlet_theta_arb(res, G, chi, x, prec);
|
|
acb_init(eps);
|
|
acb_conj(eps, res);
|
|
acb_div(res, res, eps, prec);
|
|
|
|
if (dirichlet_char_is_real(G, chi))
|
|
arb_zero(acb_imagref(res));
|
|
|
|
arb_clear(x);
|
|
acb_clear(eps);
|
|
}
|
|
|
|
void
|
|
acb_dirichlet_root_number(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
|
|
{
|
|
if (dirichlet_conductor_char(G, chi) < G->q)
|
|
{
|
|
flint_printf("root number: need primitive character\n");
|
|
flint_abort();
|
|
}
|
|
else if (G->num > 1)
|
|
{
|
|
acb_t iq;
|
|
acb_init(iq);
|
|
acb_dirichlet_gauss_sum_order2(iq, G, chi, prec);
|
|
acb_dirichlet_gauss_sum(res, G, chi, prec);
|
|
acb_div(res, res, iq, prec);
|
|
acb_clear(iq);
|
|
}
|
|
else
|
|
{
|
|
acb_dirichlet_root_number_theta(res, G, chi, prec);
|
|
}
|
|
|
|
if (dirichlet_char_is_real(G, chi))
|
|
arb_zero(acb_imagref(res));
|
|
}
|